The Kinetics of Oscillating Reactions Laboratory Experiment for Physical Chemistry Richard F. ~eika,' Gary Olsen, Lindsay Beavers, and J. A. ~ r a e ~ e r ' University of Pittsburgh at Bradford,Bradford, Pittsburgh, PA 16701 Oscillating reactions are among the most fascinating chemical demonstrations (1).The theory of these reactions are discussed in physical chemical texts by Atkins (2) and Alberty (3). Although no similar experiment appears in any of the physical chemical lab manuals currently available, descriptions of many oscillating chemical and physical phenomenon have been published for classroom use (1,4-6). Several videotapes are also available. (7-10) This experiment presents chemical dynamic relationships and promotes the use of computers for analysis (11). Conditions for Osciilatory Behavior Three conditions are required for oscillatory behavior (12). The reactions must not be near thermodvnamic eauilibrium. There must he a npecles that s autocatalytic,or there must be cross-catalysis between two steps m the system. ~
~
1 MINUTE
m.0
~1.60
75.00
111.10
1m.00
There should be two steady states for the system at its initial conditions. Although oscillations are most readily apparent in open systems (e.g., heartbeats and firefly flashes), closed systems also may show such behavior for a limited time, until thermodynamic equilibrium is achieved. Nitrogen Gas Oscillator Gaseous nitrogen is produced as in eq 1. NH4Yaq) + NOzdaq) + Nz(gas)+ 2HzO(aq)
The experimental liquid procedure has previously been reported (13). The mixture, when stirred gently, effervesces periodically producing pressure spikes that can be recorded with a pressure transducer (14). This yields an 0scillation record, as in Figure 1. Alternately, a He-Ne laser beam is transmitted in the clear solution but scattered upon effervescence. A photodiode may be attached to a data-acquisition board. Best results are for thermostated, stabilized solutions that show the behavior (see Figure 2) of an open system with the following rate equations. The following sequence of gas release in a supersaturated solution, thmugh homogeneous nucleation and subsequent bubble growth and escape (I),can be used as the basis for a mechanism for this oscillator.
Nz(buhbles)+ Nz(soln)
2Nz(largwbubbles)
Tim.
Figure 1. Computer data chart of pressure-transducer voltage produced with the reaction in equation 1 followingreference 13.
596
Journal of Chemical Education
(1)
'Authors to whom wrreswndence should be addressed.
(4)
Figure 2. Computer oscillatory behavior for reaction 1 using equations 14 and 15. Nz(1arger bubbles) Z? Nz(gas)
(5)
The mechanism can be simulated with eqs 6-11 after Escher (15).
Figure 3. Limit cycle for reaction 1 using equations 14 and 15. Math modeling is simplified by reducing equations 12 and 13 by setting
where
and For this sequence, eqs 12 and 13 are the coupled rate. The dimensionless rate equations are eqs 14 and 15 with (kd2 = (kA(kzB)
These steps can be used to demonstrate the oscillating behavior shown in eqs 2 6 by letting A = F = N2(soln) X = Nz(nuclei) Y = N2(bubbles) B = D = 2Nz(soln) C = 2N&3s) E = Nz(gas)
Then
and
These equations model a well-defined oscillation as shown in Figure 2, with E = 1and p = 0.08 from Escher (15). Ndnuclei) and Nz(bubhles)exhibit the same kinetic behavior, that is
&-* d7
The first step is eq 2. It is catalyzed by N~(nuclei),so A "Nz(s(soln)" + 2X "Nz(nuelei)"+ 3X TTz(nuclei)" which is the same as eq 6. Equation 7 is obtained by adding eqs 2 and 4 withX and Y. Equation 8 is obtained by adding eqs 4 and 2 to 2 times eq 5. Equation 9 is obtained by adding eqs 3,5, and 2 with X as a catalyst. Equation 10 is eq 2. Finally, eq 11 is obtained by adding eq 3 with 2 times eq 5.
d7
and kzB= k3 Equation 6 is autocatalytic and eq 8 is a simple bimolecular step, consistent with the model. p = 0.08 which is required for oscillating behavior. Then k3 = (0.08 + 0.02)klA Volume 69 Number 7 July 1992
597
Comparing - the abscissas of Figures 1and 2 shows that To= 0.5 s, .r = 2, and k4D = 29'. Also,
p = (kdXkd2 (k4D2)(k$)
a = k$(k3f
(k4D2)(k&
The solution oscillates from unsaturation to supersaturation, and both N2(nuclei)and N2(bubbles) ari formed upon saturation. Thus,
Q,dw d~
dr
Also, once the reaction starts, oscillation is very quickly established. This is reflected in the model by the rapid convergence to the limit cycle for this mechanism, as shown in Figure 3. Both of these facts are in agreement with this analysis. once the experimental oscillatory record has been obtained. the students may refine the kinetic model to determine & and p in eqs 14 and 15. Throughout the time of periodic oscillation, a is essentially constant. The value of a may range from 0 to 2.7; at 2.995 the model becomes a steady state. Varying a essentially changes the width of computed pressure spikes. P affects the time between the pressure spikes. It may range from 0 to 2.5; at 3.0 the model collapses into chaos. The rate constant k3 is related to all other parameters below.
k~ = ~(k,~)~(dr,)"
If the concentration of N2(nuclei)ranges throughlo% of that of Nz(soln),then it is near 6 x lo5 M. Then this is the value of X, and Yo, and kg is on the order of lo4 M-' s-'. A normalization factor of lo4 must be applied to the model values in order to coincide with the experimental oscillation results. The modeling was performed with Stella software (16). We provide a Macintosh disk that illustrates this oscillating reaction in more detail and also a MathCAD disk for PC's. Acknowledgment A Faculty Development Grant of the University of Pittsburgh at Bradford is gratefully acknowledged. Literature Cited. 1. Scott, E. s.;Sehreiner, R.; S h a r p L. R.: S h a L h a s k , B. 2.Em",C.E. In CkemIml lkmonsfmflana:Shakhashiri, B. 2.. Ed.; University of msconsul: Madism, WI, 1985;VolZ. pp 232303. 2. A t k n , P. W. Physiml Ckemlstry. 4th ed.; Freeman: NewYorh 1989. 3. Albert%R. A.Phyaical Chemistq, 7th ed.;Wiley Neu. York, 1987. 4. Summerlin, L R.:Ealy. J r , J. L. ChemlurlDema~tmlions, 2nd 4.;ACS: Washington,DC,1988;Vol. 1, pp 112-114. 5. Summerlin, L.R.; Ealy, J r , J. L.Chemlml Demonsfmtions ACS: Washington. DC, 1987;Vol.2, p 47. 6. Bodneq C.M.; Keyea. K. L.: Greenblue, T J. l7mPurdue UniuersifyLeefun I*monsimfionMonuol: Wiley: New YaL,1989. 7. V u l e o D o m o ~ f m i i o n s ~Gemmi m Chemistry;Freeman: New Yark, 1989. 8. Heath Chemiml k t z n DpmonsfmtLma; Heath: L d g t m , MA, 1988. lkmonstmtiom in ~ ~ ~ i l i b t iuniversity ,.~; ofnmoia, mm.d meoten9. ter: Champaign, IL. 1987. lo. Summerh, L. R.; Ealx Jr., J. L.C l m - U p on C k e m b ~ : C k e m i m l D e m o n s t m d d ; ACS: Washingtan, DC, 1991. 11. Lippineotr, W. T. InEssoysinPhy~lcalChemistry;Lippineon,W.T,Ed.;ACS: Waahington, DC, 1968,pp 1-2. 12. Tolman,C.A. :J a c h n , N . B . l n E s s a yi~i P h y ~ i c o Ckemistry:LippineottW.T.,Ed.; l ACS: Washingtan, DC. 1988, pp 2627. 13. Kaushik, S. M.;Yuan,Z.;Noyes,R.M. J Chem Educ 1986.63.76. 14. An wcellent pressure wage is the Minrhelic Catalog No. N92, Dwyer Instrumen& inc, Michigan City. IN 46360. 15. Escher, C. 2.Physik B 1979.35,351. 16. Stella, Version 2; High Performance System: Hanover, NH 03755.
n,
598
Journal of Chemical Education
